LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
restart:with(plots):with(Student[Calculus1]):
ApproximateInt(sin(x^2),x=0..1,output=plot,method=left);
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
ApproximateInt(sin(x^2),x=0..1,output=plot,method=right);
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
ApproximateInt(sin(x^2),x=0..1,output=plot,method=midpoint);
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
ApproximateInt(sin(x^2),x=0..1,output=plot,method=trapezoid);
int(sin(x^2),x=0.0..1);
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JCIrPElvLUohIzU=
f:=x->x^2;
a:=0;
b:=2;
int(f(x),x=a..b);
evalf(%);
Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiQpRiQiIiMiIiJGJUYlRiU=
IiIh
IiIj
IyIiKSIiJA==
JCIrbm1tbUUhIio=
Approximate Integral Values for Different Methods and n values for f(x)=x^2 on the interval [0,2].
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
Value of the Errors for the Above Approximate Integrals
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
ApproximateInt(ln(x)/(1+x),x=1..2,partition=10,output=plot,method=left);
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
ApproximateInt(ln(x)/(1+x),x=1..2,partition=10,output=plot,method=right);
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
ApproximateInt(ln(x)/(1+x),x=1..2,partition=10,output=plot,method=midpoint);
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
ApproximateInt(ln(x)/(1+x),x=1..2,partition=10,output=plot,method=trapezoid);
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int(ln(x)/(1+x),x=1..2);evalf(%);
LCgqJiMiIiIiIzdGJSlJI1BpRyUqcHJvdGVjdGVkRyIiI0YlRiUtSSZkaWxvZ0c2JEYpSShfc3lzbGliRzYiNiMiIiRGJSomLUkjbG5HRi02I0YqRiUtRjRGMEYlRiU=
JCIrdG4/czkhIzU=
diff(diff(ln(x)/(1+x),x),x);
plot((x*(1+x)^2*(-ln(x))-(1+x-x*ln(x))*((1+x)^2+x*2*(1+x)))/(x^2*(1+x)^4),x=1..2);
LCgqJilJInhHNiIiIiMhIiIsJiIiIkYqRiVGKkYoRigqKEYnRipGJUYoKUYpRidGKEYoKihGJ0YqLUkjbG5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiY2I0YlRiopRikiIiRGKEYq
LSUlUExPVEc2KC0lJ0NVUlZFU0c2JDdTNyQkIiM1ISIiJCEjNSEiIjckJCIybW1tVDooekA1ISM7JCExekUiUndQTloqISM7NyQkIjJNTGU5dWkyLyIhIzskITFzIUhBXWFSLyohIzs3JCQiMm5tO3pfIjRpNSEjOyQhMWFiW18qZitmKSEjOzckJCIybm07YXBoTjMiISM7JCEwWylvIlJIPzspISM6NyQkIjJNTGUqPSlIXDUiISM7JCExPUMjekBxRHcoISM7NyQkIjJubSJ6LzN1QzYhIzskITE4KTRxXzVUVCghIzs3JCQiLkRKJFJEWDYhIzckITF2XG1OUipRMighIzs3JCQiMm1tInpSJ29rOyIhIzskITFARSQzUD1EdSchIzs3JCQiLkQxSjp3PSIhIzckITEqb1xZNFw5VichIzs3JCQiMk5MTDNFbiQ0NyEjOyQhMTk+MUhrM0loISM7NyQkIjJtbTsvUkUmRzchIzskITFYUGk5KDMjemUhIzs3JCQiLEQuJjRdNyEjNSQhMVQ/SWBEKj5oJiEjOzckJCIyKioqKipcUEF2cjchIzskITFBKj0iKkgzKWVgISM7NyQkIix2J0hpI0giISM1JCEwRXBtVyI+R14hIzo3JCQiMm1tInoqZXY6SiIhIzskITEoZkIueTUlSFwhIzs3JCQiMkxMTDM0N1RMIiEjOyQhMUImKW8hUXlgcSUhIzs3JCQiMktMTExZLktOIiEjOyQhMVFmbj1KVkRYISM7NyQkIi5EIm83VHY4ISM3JCExOTBmIik+dUVWISM7NyQkIjJLTEwkUSpvXVIiISM7JCExRHU4amojKWZUISM7NyQkIi5EIj1sajs5ISM3JCEyTycqbykzPngmKVIhIzw3JCQiLnZWJlI8UDkhIzckITFzLEY5QUxHUSEjOzckJCIyTEwkZTlFZ2U5ISM7JCEyJCpHWSlSKW9AbiQhIzw3JCQiMk1MZVIiM0d5OSEjOyQhMid5UCVlQkljYCQhIzw3JCQiMm5tOy9UMSYqXCIhIzskITFRTT1zbkgmUiQhIzs3JCQiMm1tInpSUWJAOiEjOyQhMWVrVihSOW5EJCEjOzckJCIyKSoqXCg9PlkyYSIhIzskITFlKlE+dyhwVEohIzs3JCQiMm1tO3pYdTljIiEjOyQhMkNoJHkvQy1CSSEjPDckJCIrJnkpKUdlIiEiKiQhMSZSVz1LTmghSCEjOzckJCItREUmUVFnIiEjNiQhMldYNlVoIjQoeiMhIzw3JCQiLkQieSUzVGkiISM3JCExJT14X1MzanAjISM7NyQkIi12LltoWTshIzYkITExSzYybGEqZSMhIzs3JCQiMkxMTCRReCRvbSIhIzskITFvP1cyMil6XCMhIzs3JCQiMioqKioqXFArVilvIiEjOyQhMjp5RmAnZV8vQyEjPDckJCIybW0ienBlKnpxIiEjOyQhL2NcRSQpW0JCISM5NyQkIixEXCdRSDwhIzUkITE0QyJcMGAnUUEhIzs3JCQiMkpMZTlTOCZcPCEjOyQhMltiOmw/TkE7IyEjPDckJCIuRDEjPWJxPCEjNyQhMm5BSiIpWzBkMyMhIzw3JCQiMkxMTDNzPzZ6IiEjOyQhMjAveCxaRlMsIyEjPDckJCIuREpYYUUiPSEjNyQhMkQwKkdkKVtAJT4hIzw3JCQiMm1tbW0qUlJMPSEjOyQhMkZIbCNSZCNlKD0hIzw3JCQiMmxtO2E8LlkmPSEjOyQhMVFTayl5KzMiPSEjOzckJCIyTExlOXRPYyg9ISM7JCEyOF5kTypIKCpbPCEjPDckJCIrJlFrXCo9ISIqJCEyO3pPdV8jUSVwIiEjPDckJCIyS0wkM2RnNjw+ISM7JCExOyhcaEQzVmoiISM7NyQkIjJsbW1teEdwJD4hIzskITFsKEc3RUZGZSIhIzs3JCQiLkQib0swZT4hIzckITFVOWBCNScpSDohIzs3JCQiLnY9NXMjeT4hIzckITApM3RWZEEiWyIhIzo3JCQiIz8hIiIkITJWNnUlKTMtNVYiISM8LSUmQ09MT1JHNiYlJFJHQkckIiM1ISIiJCIiISEiIiQiIiEhIiItJSVWSUVXRzYkOyQiIzUhIiIkIiM/ISIiJShERUZBVUxURy0mJSZfQVhJU0c2IyIiIjYmLSUmQ09MT1JHNiYlJFJHQkckIiIhISIiJCIiISEiIiQiIiEhIiItJSpMSU5FU1RZTEVHNiMiIiEtJSpUSElDS05FU1NHNiMiIiItJS1UUkFOU1BBUkVOQ1lHNiMkIiIhISIiLSYlJl9BWElTRzYjIiIjNiYtJSZDT0xPUkc2JiUkUkdCRyQiIiEhIiIkIiIhISIiJCIiISEiIi0lKkxJTkVTVFlMRUc2IyIiIS0lKlRISUNLTkVTU0c2IyIiIi0lLVRSQU5TUEFSRU5DWUc2IyQiIiEhIiItJStBWEVTTEFCRUxTRzYlLUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHNiI2NVEieDYiLyUnZmFtaWx5R1EhNiIvJSVzaXplR1EjMTA2Ii8lJWJvbGRHUSZmYWxzZTYiLyUnaXRhbGljR1EldHJ1ZTYiLyUqdW5kZXJsaW5lR1EmZmFsc2U2Ii8lKnN1YnNjcmlwdEdRJmZhbHNlNiIvJSxzdXBlcnNjcmlwdEdRJmZhbHNlNiIvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXTYiLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV02Ii8lJ29wYXF1ZUdRJmZhbHNlNiIvJStleGVjdXRhYmxlR1EmZmFsc2U2Ii8lKXJlYWRvbmx5R1EmZmFsc2U2Ii8lKWNvbXBvc2VkR1EmZmFsc2U2Ii8lKmNvbnZlcnRlZEdRJmZhbHNlNiIvJStpbXNlbGVjdGVkR1EmZmFsc2U2Ii8lLHBsYWNlaG9sZGVyR1EmZmFsc2U2Ii8lNnNlbGVjdGlvbi1wbGFjZWhvbGRlckdRJmZhbHNlNiIvJSxtYXRodmFyaWFudEdRJ2l0YWxpYzYiUSE2Ii0lJUZPTlRHNiUlKERFRkFVTFRHJShERUZBVUxURyIjNS0lJVJPT1RHNictJSlCT1VORFNfWEc2IyQiJD8mISIiLSUpQk9VTkRTX1lHNiMkIiQ/JSEiIi0lLUJPVU5EU19XSURUSEc2IyQiJStNISIiLSUuQk9VTkRTX0hFSUdIVEc2IyQiJV1NISIiLSUpQ0hJTERSRU5HNiI=
Value of the Errors for the Above Approximate Integrals
ApproximateInt(cos(x^2),x=0..1,partition=8,output=sum,method=trapezoid);
evalf(%);
ApproximateInt(cos(x^2),x=0..1,partition=8,output=sum,method=midpoint);
evalf(%);
LCQtSSRTdW1HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JCwmLUkkY29zR0YlNiMsJCokSSJpR0YoIiIjIyIiIiIja0YzLUYsNiMqJCwmRjAjRjMiIilGOUYzRjFGMy9GMDsiIiEiIigjRjMiIzs=
JCIrUSVHTC0qISM1
LCQtSSRTdW1HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JC1JJGNvc0dGJTYjKiQsJkkiaUdGKCMiIiIiIikjRjEiIztGMSIiIy9GLzsiIiEiIihGMA==
JCIrciYqPmMhKiEjNQ==
ApproximateInt(cos(x^2),x=0..1,partition=71,output=sum,method=trapezoid);
evalf(%);
ApproximateInt(cos(x^2),x=0..1,partition=50,output=sum,method=midpoint);
evalf(%);
LCQqJiMiIiIiJFUiRiUtSSRTdW1HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JCwmLUkkY29zR0YpNiMsJComI0YlIiVUXUYlKUkiaUdGLCIiI0YlRiVGJS1GMDYjKiQpLCYqJiNGJSIjckYlRjdGJUYlRj9GJUY4RiVGJS9GNzsiIiEiI3FGJUYl
JCIrcFQnXC8qISM1
LCQqJiMiIiIiI11GJS1JJFN1bUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkLUkkY29zR0YpNiMqJCksJiomRiRGJUkiaUdGLEYlRiUjRiUiJCsiRiUiIiNGJS9GNTsiIiEiI1xGJUYl
JCIrcUdfWCEqISM1
diff(diff(diff(diff(cos(x^2),x),x),x),x);
LCgqKCIjOyIiIi1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjKiQpSSJ4R0YrIiIjRiVGJSlGLyIiJUYlRiUqKCIjW0YlLUkkc2luR0YoRixGJUYuRiVGJSomIiM3RiVGJkYlISIi
evalf(76/(180*8^4));
evalf((760000/180)^(1/4));
JCIrc2YiMy4iISM4
JCIrbEEkNDEpISIq
ApproximateInt(cos(x^2),x=0..1,partition=8,output=plot,method=simpson);
ApproximateInt(cos(x^2),x=0..1,partition=8,output=sum,method=simpson);
evalf(%);
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LCQtSSRTdW1HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JCwoLUkkY29zR0YlNiMsJCokSSJpR0YoIiIjIyIiIiIja0YzLUYsNiMqJCwmRjAjRjMiIikjRjMiIztGM0YxIiIlLUYsNiMqJCwmRjBGOUY5RjNGMUYzL0YwOyIiISIiKCNGMyIjWw==
JCIrQ0RDWCEqISM1
int(cos(x^2),x=0.0..1);
JCIrekJDWCEqISM1
ApproximateInt(sin(3*x)*exp(2*x),x=0..2,partition=6,method=simpson,output=plot);
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